Acoustic Instability of the Slab Rocket Motor

Fischbach, Sean R.; Majdalani, Joseph; Flandro, Gary A.

doi:10.2514/1.14794

Cited by 44 publications

(19 citation statements)

References 45 publications

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“…1,2 Owing to this fact, analytical methodologies put forward to describe flow oscillations lean heavily on the assumption of small acoustic disturbances. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] Contrary to this assumption, however, a vast body of experimental evidence conveys a dissimilar picture, specifically, one involving large amplitude oscillations with steep gradients in flow variables. For example, in the extensive experimental studies of Clayton, Sotter, and co-workers, [18][19][20][21] a heavily instrumented, laboratory scale, 20 000 lbf thrust engine was used to investigate high amplitude tangential oscillations.…”

Section: Introductionmentioning

confidence: 99%

Acoustic streaming in simplified liquid rocket engines with transverse mode oscillations

2010

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This study considers a simplified model of a liquid rocket engine in which uniform injection is imposed at the faceplate. The corresponding cylindrical chamber has a small length-to-diameter ratio with respect to solid and hybrid rockets. Given their low chamber aspect ratios, liquid thrust engines are known to experience severe tangential and radial oscillation modes more often than longitudinal ones. In order to model this behavior, tangential and radial waves are superimposed onto a basic mean-flow model that consists of a steady, uniform axial velocity throughout the chamber. Using perturbation tools, both potential and viscous flow equations are then linearized in the pressure wave amplitude and solved to the second order. The effects of the headwall Mach number are leveraged as well. While the potential flow analysis does not predict any acoustic streaming effects, the viscous solution carried out to the second order gives rise to steady secondary flow patterns near the headwall. These axisymmetric, steady contributions to the tangential and radial traveling waves are induced by the convective flow motion through interactions with inertial and viscous forces. We find that suppressing either the convective terms or viscosity at the headwall leads to spurious solutions that are free from streaming. In our problem, streaming is initiated at the headwall, within the boundary layer, and then extends throughout the chamber. We find that nonlinear streaming effects of tangential and radial waves act to alter the outer solution inside a cylinder with headwall injection. As a result of streaming, the radial wave velocities are intensified in one-half of the domain and reduced in the opposite half at any instant of time. Similarly, the tangential waves are either enhanced or weakened in two opposing sectors that are at 90°angle to the radial velocity counterparts. The second-order viscous solution that we obtain clearly displays both an oscillating and a steady flow component. The steady part can be an important contributor to wave steepening, a mechanism that is often observed during the onset of acoustic instability.

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Section: Introductionmentioning

confidence: 99%

Acoustic streaming in simplified liquid rocket engines with transverse mode oscillations

2010

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“…Due to the simplicity of its expression and its pseudo-viscous disposition to satisfy the no-slip condition at the propellant sidewall, it has been used at the foundation of a large number of investigations aimed at describing acoustic wave disturbances (Flandro et al 2 and Fischbach et al 3,4 ), particle-mean flow interactions (Féraille and Casalis, 5 Bhatia et al, 6 and Féraille et al 7 ), and both vorticoacoustic and hydrodynamic instabilities in SRMs (Ugurtas et al, 8 Fabignon et al, 9 and Boyer et al 10,11 ), where it has been relied upon to represent the bulk gaseous motion. Additional examples abound and one may cite the works of Griffond et al, 12 Majdalani et al, 13 Abu-Irshaid et al, 14 and Chedevergne et al 15,16 According to this traditional model, the steady-state velocity and vorticity distributions remain strictly orthogonal, thus giving rise to the onset of complex lamellar vector fields.…”

Section: Introductionmentioning

confidence: 99%

On Steady Trkalian High Speed Flows: Swirling Compressible Motions in Rockets with Headwall Injection

Cecil¹,

Majdalani²,

Batterson³

2015

51st AIAA/SAE/ASEE Joint Propulsion Conference

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This work considers the wall-injected swirling motions evolving inside a right-cylindrical solid rocket motor (SRM) with and without headwall injection and, alternatively, a hybrid rocket engine (HRE) with an axisymmetric oxidizer showerhead at its forward closure. The bulk gaseous motion is modeled as a non-reactive, inviscid flow with a swirl velocity component that increases linearly along the axis of the chamber. Our approach is initiated from the compressible Bragg-Hawthorne equation, which is systematically solved using Rayleigh-Janzen perturbation expansions, to the extent of producing closed-form semi-analytical approximations for the stream function of a Trkalian motion from which all other flow attributes may be readily inferred. In the process, the case of a similarity-conforming headwall injection profile is considered, where the axial flow entering the chamber at the forward end enables us to simulate conditions associated with an idealized solid rocket motor with a reactive fore-end closure, or a simplified hybrid rocket engine with an oxidizer flux along its chamber's head-end section. Results are then compared to their counterparts obtained using a strictly incompressible Trkalian profile (Majdalani, J., and Fist, A., Improved Mean Flow Solution for Solid Rocket Motors with a Naturally Developing Swirling Motion, AIAA Paper 2014-4016, July 2014). They are also benchmarked against available compressible solutions in an effort to characterize the dilatational effects that are precipitated by flow acceleration in long rocket chambers or chambers with sufficiently large sidewall injection. Besides the stream function, the velocity, pressure, temperature, and density are evaluated over a range of physical parameters corresponding to both SRM and HRE flows. Finally, the distortions affecting the velocity profiles are characterized and shown to result in a blunter motion near the center and a steeper curvature near the sidewall as a consequence of high speed flow acceleration. In comparison to nonswirling complex-lamellar solutions, we find the Trkalian solution to be generally faster and therefore able to reach sonic conditions in a shorter distance from the headwall.

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“…Note that low-magnitude pressure waves due to vortex-shedding from segmented/gapped components in the motor chamber are not included (here) in this more traditional category of nonlinear axial instability. Studies of nonlinear axial combustion instability have ranged from numerous experimental test firing series on the one hand [1][2][3], and linear/nonlinear acoustic theory modeling on the other (largely, the analysis producing frequency-based standing wave solutions for a given chamber geometry, but without some useful quantitative information) [4][5][6][7]. On occasion, researchers have employed a numerical modeling approach, to work towards a more comprehensive quantitative understanding of the physics involved (the numerical model producing a traveling wave solution to a limit wave amplitude and corresponding small or larger dc shift, typically a time-based result evolving from an initial pulse disturbance introduced into the chamber flow) [8,9].…”

Section: Introductionmentioning

confidence: 99%

Use of Reactive Particles for Solid Rocket Combustion Instability Suppression

Greatrix¹

2014

50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference

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Research towards predicting and quantifying undesirable transient axial combustion instability symptoms in solid-propellant rocket motors necessitates a comprehensive numerical model for internal ballistic simulation under dynamic flow and combustion conditions. In the present investigation, a numerical evaluation of the usage of reactive aluminum particles for the suppression of axial shock wave development is brought forward, for a motor whose instability symptom driving mechanisms are based on transient combustion response and structural-vibration-induced normal acceleration. A primary focus is placed on evaluating the qualitative trends associated with the use of aluminum particles that in general diminish in size as they move downstream in the central internal flow. The particle size regression is stipulated to occur at a nonuniform rate, through an evaporation law that is governed by the particle's current diameter. Individual transient internal ballistic simulation runs for a reference composite-propellant cylindrical-grain motor show the evolution of the axial pressure wave for a given initiating pressure disturbance, particle loading, and initial particle size. The limit pressure wave magnitudes at a later reference time in a given firing simulation run are collected for a series of runs, in order to assist in the evaluation of identifiable trends. The numerical results demonstrate that the ability of the particles to suppress axial wave development can be effective, but in general, not nearly as effective when comparing to the constant-diameter inert particle case, for the same particle loading. There may be some advantage in using a larger starting reactive particle size relative to the reference inert case, for improved overall symptom suppression, to a certain extent. However, increasing the reactive particle loading may ultimately be the only feasible means for reaching a desired symptom suppression level. Nomenclature A= local core cross-sectional area, m 2 a = gas sound speed, m/s a R = longitudinal (or lateral) acceleration, m/s 2 a n = normal acceleration, m/s 2 b = nonequilibrium sound speed of two-phase mixture C = de St. Robert coefficient, m/s-Pa n C m = particle solid specific heat, J/kg-K C p = gas specific heat, J/kg-K C pp = reactive particle gas specific heat, J/kg-K C s = specific heat, solid phase, J/kg-K D i = drag of gas on a particle from i th particle set, N d = local core hydraulic diameter, m d mi = mean particle diameter for i th particle set, m d m,o = initial particle diameter, m E = local total specific energy of gas in core flow, J/kg E pi = local total specific energy, i th particle set in flow, J/kg f = frequency, Hz, or Darcy-Weisbach friction factor Propulsion and Energy Forum G a = accelerative mass flux, kg/m 2 -s h = convective heat transfer coefficient, W/m 2 -K )H s = net surface heat of reaction, J/kg K b = burn rate limiting coefficient, s -1 k = gas thermal conductivity, W/m-K k r = particle evaporation coefficient, s m / p n k s = thermal conductivity, solid ph...

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Acoustic Instability of the Slab Rocket Motor

Cited by 44 publications

References 45 publications

Acoustic streaming in simplified liquid rocket engines with transverse mode oscillations

Acoustic streaming in simplified liquid rocket engines with transverse mode oscillations

On Steady Trkalian High Speed Flows: Swirling Compressible Motions in Rockets with Headwall Injection

Use of Reactive Particles for Solid Rocket Combustion Instability Suppression

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